es tan clásica y tan jazzy, como contemporánea

English translation: It\'s classical and jazzy, and yet contemporary

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if the music you are talking about is 'serious' jazz then I would avoid the term 'jazzy' in English, it tends to be used for styles such as easy listening, fusion, r&b, hip-hop etc, ie to denote a jazz influence.

It should be noted that “clásica/classical” contrasts more clearly with “contemporánea/contemporary (modern)” than “jazzy” does. To me, this seems to be the basic problem to your question. To complicate things further:
(a) there is of course a period of “classical jazz” which deserves to be distinguished from e. g. “modern/contemporary” jazz music
(b) modernism and postmodernism differ from both “classical” and “jazzy” approaches to music at least through some kind of “awareness” or “sophistication” of past approaches (deliberate citation, eclecticism, “crossover”, etc.)
(c) in the US (in contrast to the European tradition), there is little to no distinction between “classical/serious” and “popular/contemporary” music.

In translating your phrase, and lacking further context, I would try to give all 3 attributions equal weight (as in the original), and trust in the self-explanatory description that follows the third one, which refers to the “contemporary nature” of the “version” in question.